A Two-Stage Decomposition Approach for AC Optimal Power Flow

Tu, Shenyinying; Wachter, Andreas; Wei, Ermin

doi:10.1109/tpwrs.2020.3002189

Title: A Two-Stage Decomposition Approach for AC Optimal Power Flow

Abstract

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. Furthermore, this paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 millionmore » buses.« less

Authors:

^[1];

^[1]

Northwestern Univ., Evanston, IL (United States)

Publication Date:: Fri Jun 12 00:00:00 EDT 2020

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1844144

Report Number(s):: LA-UR-20-24243
Journal ID: ISSN 0885-8950

Grant/Contract Number:: 89233218CNA000001

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Power Systems

Additional Journal Information:: Journal Volume: 36; Journal Issue: 1; Journal ID: ISSN 0885-8950

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 24 POWER TRANSMISSION AND DISTRIBUTION; Optimal power flow; decomposition; transmission networks; distribution networks; primal-dual interior point method; two-stage optimization; smoothing technique; stochastic optimization

Citation Formats


                    Tu, Shenyinying, Wachter, Andreas, and Wei, Ermin. A Two-Stage Decomposition Approach for AC Optimal Power Flow.  United States: N. p., 2020. 
Web.  doi:10.1109/tpwrs.2020.3002189.

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                    Tu, Shenyinying, Wachter, Andreas, & Wei, Ermin. A Two-Stage Decomposition Approach for AC Optimal Power Flow.  United States.  https://doi.org/10.1109/tpwrs.2020.3002189

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                    Tu, Shenyinying, Wachter, Andreas, and Wei, Ermin. Fri .  
"A Two-Stage Decomposition Approach for AC Optimal Power Flow".  United States.  https://doi.org/10.1109/tpwrs.2020.3002189.  https://www.osti.gov/servlets/purl/1844144.

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@article{osti_1844144,

  title        = {A Two-Stage Decomposition Approach for AC Optimal Power Flow},

  author       = {Tu, Shenyinying and Wachter, Andreas and Wei, Ermin},

  abstractNote = {The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. Furthermore, this paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.},

  doi          = {10.1109/tpwrs.2020.3002189},

  journal      = {IEEE Transactions on Power Systems},

  number       = 1,

  volume       = 36,

  place        = {United States},

  year         = {Fri Jun 12 00:00:00 EDT 2020},

  month        = {Fri Jun 12 00:00:00 EDT 2020}

}

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Title: A Two-Stage Decomposition Approach for AC Optimal Power Flow

Abstract

Citation Formats

Optimal thermal generating unit commitment: a review journal, October 1998

A Primal-Dual Interior Point Method for Optimal Power Flow Dispatching journal, July 2002

A parallel primal-dual interior-point method for DC optimal power flow conference, June 2016

Generic Existence of Unique Lagrange Multipliers in AC Optimal Power Flow journal, October 2018

An interior algorithm for nonlinear optimization that combines line search and trust region steps journal, November 2005

A local convergence analysis of bilevel decomposition algorithms journal, June 2006

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Hierarchical coordination of TSO-DSO economic dispatch considering large-scale integration of distributed energy resources journal, June 2017

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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal, April 2005

Multi-Area Unit Scheduling and Reserve Allocation Under Wind Power Uncertainty journal, July 2014

Energy Management Systems in Microgrid Operations journal, October 2012

On Decomposition Methods for a Class of Partially Separable Nonlinear Programs journal, February 2008

Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence journal, March 2014

Master–Slave-Splitting Based Distributed Global Power Flow Method for Integrated Transmission and Distribution Analysis journal, May 2015

Optimal power flow: a bibliographic survey I: Formulations and deterministic methods journal, April 2012

A survey of the optimal power flow literature journal, May 1991

Distributed Optimal Power Flow Using ADMM journal, September 2014

Interior-point based algorithms for the solution of optimal power flow problems journal, April 2007

A primal-dual interior point method for optimal power flow dispatching journal, August 2002

Distributed algorithms for optimal power flow problem conference, December 2012

Distributed Optimal Power Flow for Smart Microgrids journal, September 2013

Optimal distribution systems reconfiguration for radial and meshed grids journal, November 2015

MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education journal, February 2011

A Linear-Programming Approximation of AC Power Flows journal, November 2014

Coordinated Transmission and Distribution AC Optimal Power Flow journal, March 2018

A fast moving horizon estimation algorithm based on nonlinear programming sensitivity journal, October 2008

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A Survey of Relaxations and Approximations of the Power Flow Equations journal, January 2019

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Unit Commitment—A Bibliographical Survey journal, May 2004

Further developments in LP-based optimal power flow journal, January 1990

Infeasibility Detection and SQP Methods for Nonlinear Optimization journal, January 2010

Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design journal, February 2002

Knitro: An Integrated Package for Nonlinear Optimization book, January 2006

Strengthening the SDP Relaxation of AC Power Flows With Convex Envelopes, Bound Tightening, and Valid Inequalities journal, September 2017

Interior-point methods journal, December 2000

Sequential Quadratic Programming journal, January 1995

Optimal thermal generating unit commitment: a review
journal, October 1998

A Primal-Dual Interior Point Method for Optimal Power Flow Dispatching
journal, July 2002

A parallel primal-dual interior-point method for DC optimal power flow
conference, June 2016

Generic Existence of Unique Lagrange Multipliers in AC Optimal Power Flow
journal, October 2018

An interior algorithm for nonlinear optimization that combines line search and trust region steps
journal, November 2005

A local convergence analysis of bilevel decomposition algorithms
journal, June 2006

Diagonal Quadratic Approximation for Decentralized Collaborative TSO+DSO Optimal Power Flow
journal, May 2019

Hierarchical coordination of TSO-DSO economic dispatch considering large-scale integration of distributed energy resources
journal, June 2017

Coordinated Economic Dispatch of Coupled Transmission and Distribution Systems Using Heterogeneous Decomposition
journal, November 2016

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Multi-Area Unit Scheduling and Reserve Allocation Under Wind Power Uncertainty
journal, July 2014

Energy Management Systems in Microgrid Operations
journal, October 2012

On Decomposition Methods for a Class of Partially Separable Nonlinear Programs
journal, February 2008

Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence
journal, March 2014

Master–Slave-Splitting Based Distributed Global Power Flow Method for Integrated Transmission and Distribution Analysis
journal, May 2015

Optimal power flow: a bibliographic survey I: Formulations and deterministic methods
journal, April 2012

A survey of the optimal power flow literature
journal, May 1991

Distributed Optimal Power Flow Using ADMM
journal, September 2014

Interior-point based algorithms for the solution of optimal power flow problems
journal, April 2007

A primal-dual interior point method for optimal power flow dispatching
journal, August 2002

Distributed algorithms for optimal power flow problem
conference, December 2012

Distributed Optimal Power Flow for Smart Microgrids
journal, September 2013

Optimal distribution systems reconfiguration for radial and meshed grids
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MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education
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A Linear-Programming Approximation of AC Power Flows
journal, November 2014

Coordinated Transmission and Distribution AC Optimal Power Flow
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A fast moving horizon estimation algorithm based on nonlinear programming sensitivity
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Hierarchical Risk Assessment of Transmission System Considering the Influence of Active Distribution Network
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journal, November 2017

Coarse-grained distributed optimal power flow
journal, May 1997

A fast distributed implementation of optimal power flow
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journal, February 2009

A Survey of Relaxations and Approximations of the Power Flow Equations
journal, January 2019

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journal, August 2011

Unit Commitment—A Bibliographical Survey
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journal, January 1990

Infeasibility Detection and SQP Methods for Nonlinear Optimization
journal, January 2010

Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design
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Knitro: An Integrated Package for Nonlinear Optimization
book, January 2006

Strengthening the SDP Relaxation of AC Power Flows With Convex Envelopes, Bound Tightening, and Valid Inequalities
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Interior-point methods
journal, December 2000

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journal, January 1995